TRPL+K: Thick-Restart Preconditioned Lanczos+K Method for Large Symmetric Eigenvalue Problems
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چکیده
منابع مشابه
TRPL+K: Thick-Restart Preconditioned Lanczos+K Method for Large Symmetric Eigenvalue Problems
The Lanczos method is one of the standard approaches for computing a few eigenpairs of a large, sparse, symmetric matrix. It is typically used with restarting to avoid unbounded growth of memory and computational requirements. Thick-restart Lanczos is a popular restarted variant because of its simplicity and numerically robustness. However, convergence can be slow for highly clustered eigenvalu...
متن کاملThick-Restart Lanczos Method for Symmetric Eigenvalue Problems
For real symmetric eigenvalue problems, there are a number of algorithms that are mathematically equivalent, for example, the Lanczos algorithm, the Arnoldi method and the unpreconditioned Davidson method. The Lanczos algorithm is often preferred because it uses signiicantly fewer arithmetic operations per iteration. To limit the maximum memory usage, these algorithms are often restarted. In re...
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Efficiently preconditioned inexact Newton methods for large symmetric eigenvalue problems L. Bergamaschi & A. Martínez a Department of Civil, Environmental and Architectural Engineering, University of Padua, via Trieste 63, 35100 Padova, Italy b Department of Mathematics, University of Padua, via Trieste 63, 35100 Padova, Italy Accepted author version posted online: 14 Apr 2014.Published online...
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This research focuses on nding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, nding 1000 eigenpairs of a 100,000 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based algorithms and the number of desired eigenpairs is too large for most common sparse eigenvalue algorithms. I...
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The Lanczos process is a well known technique for computing a few, say k, eigenvalues and associated eigenvectors of a large symmetric n×n matrix. However, loss of orthogonality of the computed Krylov subspace basis can reduce the accuracy of the computed approximate eigenvalues. In the implicitly restarted Lanczos method studied in the present paper, this problem is addressed by fixing the num...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2019
ISSN: 1064-8275,1095-7197
DOI: 10.1137/17m1157568